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arXiv · 2504.01288

Nishida-Smoller type large solutions for the compressible Navier-Stokes equations with slip boundary conditions in 3D exterior domains

Minghong Xie·Saiguo Xu·Yinghui Zhang
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Abstract

This paper investigates the global existence of classical solutions to the isentropic compressible Navier-Stokes equations with slip boundary condition in a three-dimensional (3D) exterior domain. It is shown that the classical solutions with large initial energy and vacuum exist globally in time when the adiabatic exponent $γ>1$ is sufficiently close to 1 (near-isothermal regime). This constitutes an extension of the celebrated result for the one-dimensional Cauchy problem of the isentropic Euler equations that has been established in 1973 by Nishida and Smoller (Comm. Pure Appl. Math. 26 (1973), 183-200). To the best of our knowledge, we establish the first result on the global existence of large-energy solutions with vacuum to the compressible Navier-Stokes equations with slip boundary condition in a 3D exterior domain, which improves previous related works where either small initial energy is required or boundary effects are ignored.

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Minghong Xie, Saiguo Xu, Yinghui Zhang. 2025-04-02. Nishida-Smoller type large solutions for the compressible Navier-Stokes equations with slip boundary conditions in 3D exterior domains. https://arxiv.org/abs/2504.01288

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